A system with externally polarized dipole molecules at half-filling moving along a one-dimensional zigzag chain is studied, including ground-state phase diagrams. The dipoles are oriented in-plane. Together with the geometry of the chain, this gives rise to a bond-alternating nearest-neighbor interaction due to simultaneous attractive and repulsive interactions. By tuning the ratio between the nearest-neighbor interaction and hopping, various phases can be accessed by controlling the polarization angle. In the ultrastrong coupling limit, the system simplifies to a frustrated extended axial Ising model. For the small coupling limit, qualitative discussion of the ordering behavior using effective field theory arguments is provided. We show that when the chain angle is small, the system mostly exhibits BKT-type phase transitions, whereasa large chain angle would drive the system into a gapped (Ising) dimerized phase, where the hopping strength is closely related to the orientation of dimerized pairs.
In this dissertation, we study the many-body effects of dipoles in a quasi-one-dimensional zigzag optical lattice, which we call the zigzag chain. We study this system using the Density Matrix Renormalization Group (DMRG) method, which has established itself as the most powerful numerical method to simulate one-dimensional lattices. For the implementation of DMRG, we have used the open-source package Intelligent Tensor, or simply ITensor. The first part of this research focuses on dipoles polarized in the plane of the zigzag chain by an external electric field with the condition that the dipoles can hop around and interact with their first and second neighbors and the number of dipoles is exactly a half of the number of lattice sites. With the interactions much stronger than the hopping, the system comprises of frustrated and non-frustrated regimes owing to the combination of attractive and repulsive interactions in different directions. The consequence is a complex phase diagram featuring the trivial ferromagnetic and antiferromagnetic phases as well as the non-trivial dimerized and superfluid phases. The second part of the research deals with randomly oriented dipoles in the zigzag chain such that each lattice site has exactly one dipole and each dipole interacts with its first and second neighbors but in the absence of any hopping. We study the second system classically allowing many different orientations for each dipole in a lattice site as well as quantum mechanically by allowing a few quantized degrees of freedom to each dipole. The result is a phase diagram showing ferromagnetic, antiferromagnetic and paramagnetic phases.
We investigate the zero-temperature quantum phases of a quasi-one-dimensional zigzag chain of dipoles that are polarized in a plane by an external electric field. Since the Hamiltonian contains nearest-neighbor and next-nearest-neighbor hopping and interaction terms, this model allows frustration, which induces phases that can be interesting and unusual. By using the density matrix renormalization group algorithm, we produce a complex phase diagram. This is an extension of an earlier work by Wang et al. [Phys. Rev. A 96, 043615 (2017)].
We study polar molecules with long-range dipole-dipole interactions confined to move on a two-leg ladder for different orientations of the molecular dipole moments with respect to the ladder. Matrix product states are employed to calculate the many-body ground state of the system as a function of lattice filling fractions, perpendicular hopping between the legs, and dipole interaction strength. We show that the system exhibits zigzag ordering when the dipolar interactions are predominantly repulsive. As a function of dipole moment orientation with respect to the ladder, we find that there is a critical angle at which ordering disappears. This angle is slightly larger than the angle at which the dipoles are noninteracting along a single leg. This behavior should be observable using current experimental techniques.
We employ large-scale density matrix renormalization group calculations to study the quantum phases of dipolar molecules confined in bent (zigzag) endofullerene chains, as a function of the chain angle
γ. For LiF, ferroelectric order persists across the full range
60∘<γ180∘, with the critical effective dipole moment increasing as the chain bends and parallel alignment becomes less favorable. Near the equilateral configuration (
γ=60∘), geometric frustration drives a transition to an antiferroelectric Néel-ordered phase in which neighboring dipoles anti-align along the chain axis. We show that capturing this reorientation requires including dipolar couplings beyond the nearest-neighbor approximation, since next-nearest-neighbor interactions become equally strong at
γ=60∘. For confined water, o-D
2O reproduces both ordered phases, whereas p-H
2O -- owing to its large rotational constants -- develops no order at any chain angle despite the enhanced coordination of the bent geometry. Because a zigzag chain is the narrowest stripe of a two-dimensional lattice, these results suggest that engineered endofullerene layers could host a rich variety of dipole-ordered quantum phases beyond the ferroelectric ordering observed in previous work.
We investigate the ground-state phase diagram of the half-filled one-dimensional Hubbard model with next-nearest-neighbor hopping using the density-matrix renormalization-group technique as well as an unrestricted Hartree-Fock approximation. We find commensurate and incommensurate disordered magnetic insulating phases and a spin-gapped metallic phase in addition to the one-dimensional Heisenberg phase. At large on-site Coulomb repulsion U, we make contact with the phase diagram of the frustrated Heisenberg chain, which has spin-gapped phases for sufficiently large frustration. For weak U, sufficiently large next-nearest-neighbor hopping
t2 leads to a band structure with four Fermi points rather than two, producing a spin-gapped metallic phase. As U is increased in this regime, the system undergoes a Mott-Hubbard transition to a frustrated antiferromagnetic insulator.
The effect of next-nearest-neighbor hopping
t2 on the ground-state phase diagram of the one-dimensional Kondo lattice is studied with density-matrix renormalization-group techniques and by comparing with the phase diagram of the classical-spin variant of the same model. For a finite
t2, i.e., for a zigzag-ladder geometry, indirect antiferromagnetic interactions between the localized spins are geometrically frustrated. We demonstrate that
t2 at the same time triggers several magnetic phases which are absent in the model with nearest-neighbor hopping only. For strong
J, we find a transition from antiferromagnetic to incommensurate magnetic short-range order, which can be understood entirely in the classical-spin picture. For weaker
J, a spin-dimerized phase emerges, which spontaneously breaks the discrete translation symmetry. The phase is not accessible to perturbative means but is explained, on a qualitative level, by the classical-spin model as well. Spin dimerization alleviates magnetic frustration and is interpreted as a key to understand the emergence of quasi-long-range spiral magnetic order, which is found at weaker couplings. The phase diagram at weak
J, with gapless quasi-long-range order on top of the twofold degenerate spin-dimerized ground state, competing with a nondegenerate phase with gapped spin (and charge) excitations, is unconventional and eludes an effective low-energy spin-only theory.